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Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice


Astrakhantsev, Nikita; Westerhout, Tom; Tiwari, Apoorv; Choo, Kenny; Chen, Ao; Fischer, Mark H; Carleo, Giuseppe; Neupert, Titus (2021). Broken-Symmetry Ground States of the Heisenberg Model on the Pyrochlore Lattice. Physical Review X, 11(4):041021.

Abstract

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a resonating-valence-bond-like, many-variable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4×43 and 4×33 spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. We consider the (λ,j2/j1) parameter space, with j2, j1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

Abstract

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a resonating-valence-bond-like, many-variable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4×43 and 4×33 spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. We consider the (λ,j2/j1) parameter space, with j2, j1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

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Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > General Physics and Astronomy
Uncontrolled Keywords:General Physics and Astronomy
Language:English
Date:29 October 2021
Deposited On:23 Dec 2021 05:32
Last Modified:26 Jun 2024 01:47
Publisher:American Physical Society
ISSN:2160-3308
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1103/physrevx.11.041021
Project Information:
  • : FunderSNSF
  • : Grant IDPP00P2_176877
  • : Project TitleTopological Phases: From New Fermions to Materials and Devices
  • : FunderSimons Foundation
  • : Grant ID
  • : Project Title
  • : FunderHorizon 2020 Framework Programme
  • : Grant ID
  • : Project Title
  • : FunderH2020
  • : Grant ID701647
  • : Project TitlePSI-FELLOW-II-3i - International, Interdisciplinary and Intersectoral Postdocs
  • : FunderGalileo supercomputer
  • : Grant ID
  • : Project Title
  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)